[R] interaction terms in regression analysis

From: John S. Walker <jsw9c_at_uic.edu>
Date: Sat 10 Jun 2006 - 06:54:28 EST


My problem is I'm not sure how to extract effect sizes from a nonlinear regression model with a significant interaction term.

My data sets are multiple measurements of force response to an agonist with two superimposed treatments each having two levels. This is very similar to the Ludbrook example in Venables and Ripley.

The experiment is that a muscle is exposed to an agonist and the force response is measured. The resulting data is fit to a logistic fit (a three parameter rather than the four parameter used by Ludbrook) . This is done for each combination of two factors (treatmentA and Treatment B) each having two levels (- and +). Each set of measurements is obtained on a muscle from a different animal (i.e. each dose response curve represents an independent experiment).

The data are stored as follows:

expt treatA treatB dose force

I use a groupedData object mydata=groupedData(force ~ dose | expt)

I used an nlme obect to model the data as follows (pseudocode):

myfit <- nlme(force ~ ssThreeParLogistic(dose, upper, ed50,slope), fixed=list(ed50~factor(treatmentA)*factor(treatmentC)))

The ThreeParLogistic is a properly debugged and fully functional selfstarting object that I wrote- no problem here. I also included terms for the other terms; upper and slope, but my main focus is on the ed50 so that's all I've included here

Running an anova on the resulting object I found theA -/B- (control) to be significantly different from zero, treatment A had no significant effect, treatment B was significantly different and there was a significant interaction between treatment A and treatment B.

  The interaction term is likely to be real. The treatments are on sequential steps in a pathway and treatment A may be blocking the effect of treatment B, i.e. treatment A alone has no effect because it blocks a pathway that is not active, treatment B reduces force via this pathway and treament A therefore blocks the effect of treatment B when used together.

So back to my question
How do I extract estimates of the parameters from my model object for a specific combination of factors including the interaction term.   i.e. what is the ed50 (and std err) for A-/B-, A+/B-, A-/B+, A+/B+ ?


John S. Walker, PhD
Department of Physiology & Biophysics
University of Illinois at Chicago
835 Sth Wolcott Ave MC 901
Chicago IL 60612
USA email: jsw9c@uic.edu
phone: 1 312 355 0150
fax: 1 312 355 0261

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